# Gaussian Curve Plotting Issues

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Nicholas Fuller on 1 Jul 2021
Edited: Alan Stevens on 2 Jul 2021
Hey everyone, I am working on a normal distribution to better understand the random choice dataset I am working with. The current gaussian curve is very wrong and I am not sure why. Basically, in a group of 10,000 individuals there is a 1.3% chance they will be placed in population A, and a 98.7% chance an individual is placed in population B. I am mainly concerned with population A, as that is the population of interest. The random assignment is ran 100 times, and the values are placed in empty arrays RunSumA1 and RunSumB1.
Here is the current code and graph:
options = ['A', 'B'];
%Empty vectors for value storage
RunSumA1=[];
RunSumB1=[];
ListOneProbability=0.013;
ListTwoProbability=0.987;
totalRuns = 100;
%Storage loop from function
for k=1:totalRuns
[RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability);
end
%Converting to Column Vector
RunSumA1 = RunSumA1';
%Average, STD, Normal PDF
mu = mean(RunSumA1);
sigma = std(RunSumA1);
y = normpdf(RunSumA1, mu, sigma);
%Plot
plot(RunSumA1, y)
%Random choice function
function [RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability)
tempA1 = 0;
tempB1 = 0;
for j=1:10000
newChoice = randsample(options, 1,true, [ListOneProbability,ListTwoProbability]);
if newChoice == 'A'
tempA1=tempA1+1;
else
tempB1=tempB1+1;
end
end
RunSumA1=[RunSumA1,tempA1];
RunSumB1=[RunSumB1,tempB1];
end

the cyclist on 1 Jul 2021
Can you be more specific what you mean by "the current gaussian curve is very wrong"? Do you mean with the lines connecting all over the place? If you just plot points rather than lines, then you see the nice smooth curve:
options = ['A', 'B'];
%Empty vectors for value storage
RunSumA1=[];
RunSumB1=[];
ListOneProbability=0.013;
ListTwoProbability=0.987;
totalRuns = 100;
%Storage loop from function
for k=1:totalRuns
[RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability);
end
%Converting to Column Vector
RunSumA1 = RunSumA1';
%Average, STD, Normal PDF
mu = mean(RunSumA1);
sigma = std(RunSumA1);
y = normpdf(RunSumA1, mu, sigma);
%Plot
plot(RunSumA1, y, '.') % Changed this line to plot only the points
%Random choice function
function [RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability)
tempA1 = 0;
tempB1 = 0;
for j=1:5000 % I made the smaller, since it would not time out on the Answers forum
newChoice = randsample(options, 1,true, [ListOneProbability,ListTwoProbability]);
if newChoice == 'A'
tempA1=tempA1+1;
else
tempB1=tempB1+1;
end
end
RunSumA1=[RunSumA1,tempA1];
RunSumB1=[RunSumB1,tempB1];
end
Is that it? Or is there some other problem?
##### 1 CommentShowHide None
Nicholas Fuller on 1 Jul 2021
Yeah that was pretty much it. Kicking myself for not thinking of just using points to plot it. I was wondering if there was anything wrong with the code since it produced the interconnected lines rather than one smooth curve.

Alan Stevens on 1 Jul 2021
Edited: Alan Stevens on 2 Jul 2021
If you have 10000 individuals with a probability of 0.013 of being in group A, you would expect your curve to peak close to 130 individuals on average. Perhaps you want something like the following:
Npop = 10000;
probA = 0.013;
Ntrials = 100; %
A = zeros(Ntrials, 1);
B = zeros(Ntrials, 1);
for trial = 1:Ntrials
r = rand(Npop,1);
ir = find(r<=probA);
A(trial) = numel(ir);
B(trial) = Npop - A(trial);
end
mu = mean(A);
sigma = std(A);
disp([mu, sigma])
128.4800 10.9420
lo = 80;
hi = 180;
x = linspace(lo,hi,100);
y = exp(-0.5*((x-mu)/sigma).^2)/(sigma*sqrt(2*pi));
plot(x,y)
xlabel('Numbers in group A')
ylabel('frequency')
grid